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Ufa Mathematical Journal, 2016, Volume 8, Issue 3, Pages 8–21
DOI: https://doi.org/10.13108/2016-8-3-8
(Mi ufa322)
 

This article is cited in 4 scientific papers (total in 4 papers)

On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis

N. F. Abuzyarova

Bashkir State University, Ufa
References:
Abstract: In the work we consider a topological module $\mathcal P(a;b)$ of entire functions, which is the isomorphic image of the Schwarz space of distributions with compact supports in a finite or infinite interval $(a;b)\subset\mathbb R$ under the Fourier–Laplace transform. We prove that each weakly localizable module in $\mathcal P (a;b)$ is either generated by its two elements or is equal to the closure of two submodules of special form. We also provide dual results on subspaces in $C^\infty(a;b)$ invariant w.r.t. the differentiation operator.
Keywords: entire functions, subharmonic functions, Fourier–Laplace transform, finitely generated submodules, description of submodules, local description of submodules, invariant subspaces, spectral synthesis.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 01201456408
Received: 31.05.2016
Russian version:
Ufimskii Matematicheskii Zhurnal, 2016, Volume 8, Issue 3, Pages 8–21
Bibliographic databases:
Document Type: Article
UDC: 517.538.2+517.984.26+517.547
Language: English
Original paper language: Russian
Citation: N. F. Abuzyarova, “On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis”, Ufimsk. Mat. Zh., 8:3 (2016), 8–21; Ufa Math. J., 8:3 (2016), 8–21
Citation in format AMSBIB
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  • https://doi.org/10.13108/2016-8-3-8
  • https://www.mathnet.ru/eng/ufa/v8/i3/p8
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
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    Russian version PDF:91
    English version PDF:10
    References:45
     
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